Transpiration and spanwise wall oscillations in laminar channel flow: A path to energy savings

Judicious use of wall transpiration or spanwise wall oscillations can significantly reduce drag in pressure-driven flow. The net energy expenditure, however, is greater than for the uncontrolled laminar flow. Recent work has shown that it is theoretically possible to achieve sub-laminar net energy expenditure by combining transpiration with spanwise wall oscillations. Here, we examine this theory via direct numerical simulations of channel flow in the laminar regime. We consider streamwise-traveling waves of transpiration and spanwise wall oscillations, finding that waves whose size is on the order of the channel height can reduce drag when traveling upstream. We present a detailed analysis of the energy budget, including a scaling analysis of the dissipation induced by the control. The balance of the dissipation and flux of spanwise kinetic energy at the wall determines the net energy expenditure relative to the uncontrolled flow, and the scaling analysis suggests what levels of net energy expenditure are possible.